Animating Theories

Well it’s been quite some time since I’ve posted, which might be correlated with the academic calendar.  I’m disappointed that I haven’t been keeping up the posts this term, but I’m excited to get back to editing over winter break and get a rough cut of the documentary together.

Until then, here’s one thing I did do this term and at the end of the summer.  My professor asked me to work on visualizations for two theoretical concepts.  First was a comparison of hypotheses for how a populations range will change as temperatures increase.  Will they stay within the same temperatures, shifting their range towards the nearest pole (Climatic Envelope), or will they simply move northward (Tyranny of Thermodynamics)?  The question is really about what is limiting their range on the warmer end – is it warm temperatures or something else like competition?  Here are the visualizations:

Next is a simulation of population dynamics with two attractors (similar to equilibria but not necessarily static).  This kind of dynamic could be common in an animal that gains new resources after reaching a certain population density threshold (say, pine beetles when they reach a density capable of killing trees).  I wrote code to simulate these dynamic in python and saved pictures at each time step to make a gif.  The graph on top is the abundance over time and the graph below is the per capita growth rate ( r ) as a function of abundance, with the points flashing on it representing the actual growth rate (with stochasticity factored in).

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